Gifting income to my retired parent

1 .yes gift deed needed as share is transferred 

2. No your parents will not be taxed but returns will be filled 

And taxation will be depends on the income .

3. If they want can return you and sorry I don't understand your last query completely.

Kindly reconfirm the need for gift deed as I understand that in case of share transfer i.e. movable property,  a gift deed is advisable to maintain a proper legal record; however it is not mandatory as in case of movable property. 

Secondly, it is also requested to reconfirm whether parents need to fill income tax returns just because of receipt of gifted shares or only when their income from shares ( dividend/ Gains on sale) exceeds the basic exemption limit.